1 Technical Field
The present invention is related to the electrical rectifier field, more specifically, to the field of control techniques for the three-phase three-level boost type rectifier.
This work introduces a new control method and control circuit for a three-phase three-level boost-type rectifier. Under the proposed control method and control circuit, the rectifier performs three-phase AC-DC conversion generating sinusoidal input currents with reduced ripple and near unity power factor while balancing the two DC output voltages. The control circuit uses two triangular carriers with the same amplitude but 180 degrees phase-shifted; Trg1 is used during the positive halve cycle and Trg2 for the negative one. The advance of the method is that the switching pulses are synchronized and appropriately distributed, allowing the reduction of the input current ripple. An effective balance of the output voltage is obtained by adding a sensor that acts over the input current waveform reference. In addition, the control system features simplicity and low cost.
2 Background
With the development of power electronics technology and the generalized utilization of equipment with non-linear characteristics such as electronic rectifiers or static converters AC-DC, there have been increasing utility pollution problems produced by large distorted harmonics currents drawn from the power distribution systems [See P. Rioual and T. Deflandre, xe2x80x9cImpact on the Distribution and Transmission Systems of Harmonic Current Injection due to Capacitive Load Rectifiers in Commercial, Residential and Industrial Installationsxe2x80x9d, Conference Records of EPE""95, pp. 3.503-3.508, 1985, and Yu-Kang Lo and Neng-Chin Lia, xe2x80x9cOn Evaluating the Input Current Distortion with Current Slopes for Single-Phase Switch-Mode Rectifiersxe2x80x9d, Conference records of PESC""98, pp. 77-80, 1998]. Harmonic currents cause additional harmonic losses in the utility system and may excite electrical resonances, leading to large overvoltages; thus disturbing other sensitive loads connected to the same supply [See Ned Mohan, Tore M. Undeland, William P. Robbins, xe2x80x9cPower Electronics Converters, Applications, and Designxe2x80x9d, John Wiley and Sons, 1989].
The uncontrolled and thyristor bridge rectifiers are widely used interface between utility and power electronics systems. Although they are very simple in structure and robust in operation, they have the disadvantages of drawing a large amount of harmonic current from utility [See Hirofumi Akagi, xe2x80x9cNew Trends in Active Filters for Power Conditioningxe2x80x9d, IEEE Transactions on Industry Applications, Vol. 32, No. 6, pp. 1312-1322, 1996]. Recently the harmonics produced by such nonlinear loads have become a serious problem in many countries.
To prevent the problem to become intolerable, various standards and guidelines such as the IEEE 519 and the IEC-555, have been established which specifies limits on the magnitudes of harmonic currents and harmonic voltage distortion at various frequencies [Ned Mohan et al., op. cit.]. Simultaneously, much effort has been carried out to develop power converters with low harmonic current injection to utility and capable to control the input power factor.
Modern AC-DC converters are expected to draw sine-wave current from the mains, with power factor very close to unity. In other words it is required that the converter presents a resistive load to the mains [Javier Sebastian and Miguel Jaureguizar, xe2x80x9cTendencias Futuras en la Correccixc3x3n del Factor de Potencia en Sistemas de Alimentacixc3x3nxe2x80x9d, Conference records of CIEP""93, pp. 136-153, 1993]. In general, besides those characteristics, the target is low circuit complexity, low component stress, high power density, high efficiency, high reliability, and controllability of the output voltage.
In single-phase applications, one of the most popular power circuit schemes for power factor correction is the boost converter topology. A frond-end rectifier diode bridge followed by a boost DC-DC converter composes the topology. The technique has been extended to three-phase applications using a three-phase diode bridge and a single switch boost DC-DC converter operating in discontinuous conduction mode [A. R. Prasad, P. D. Ziogas, and S. Manias, xe2x80x9cAn Active Power Factor Correction Technique for Three-Phase Diode Rectifiersxe2x80x9d, IEEE Transactions on Power Electronics, Vol. 6, No. 1, pp. 83-92, 1991] The single active switch three-phase preregulator presents low cost and simplicity but the topology has as drawbacks high conduction losses, high switching stresses, and radio interference emission regulations resulting in a large input filter.
Circuits with multiple configuration and advanced designs are actually considered to increase the power levels and improve the generated waveforms [See A. Nabae, I. Takahashi and H. Akagi, xe2x80x9cA New Neutral-Point-Clamped PWM Inverterxe2x80x9d, IEEE Transactions on Industry Applications, vol. IA-17, No. 5, pp. 518-523, 1981; and J. W. Kolar, H. Ertl and F. C. Zach, xe2x80x9cDesign and Experimental Investigation of a Three-Phase High Power Density High Efficiency Unity Power Factor PWM (VIENNA) Rectifier Employing a Novel Integrated Power Semiconductor Modulexe2x80x9d, Conference records of APEC""96, pp. 514-523, 1996].
In fact, multilevel converters are starting to be used in industry and traction applications and its future seems promissory [See T. Katta, Y. Kurokawa, xe2x80x9cAdvanced Inverter Control System Using High Voltage IGBT for EMUxe2x80x9d Conference records of IPEC""95, pp. 1060-1065, 1995 and S. Bernet, xe2x80x9cRecent Developments of High Power Converters for Industry and Traction Applicationsxe2x80x9d Conference records of COBEP""99, pp. 3-16, 1999].
The multilevel converters present some advantages over conventional two level converters such as:
The voltage imposed across the switching devices is reduced proportionally with the number of levels. In this way, it is possible to use them in high voltage systems increasing the converter capability [R. Rojas, T. Ohnishi, T. Suzuki, xe2x80x9cPWM Control Method for a Four-Level Inverterxe2x80x9d, IEE Proceedings on Electric Power Applications, vol. 142, Issue 6, pp. 390-396, 1995].
Improve significantly the voltage and current waveforms, which results in a substantial reduction of the harmonic distortion [N. S. Choi, J. G. Cho and G. H. Cho, xe2x80x9cA General Circuit Topology of Multilevel Inverterxe2x80x9d, Conference records of PESC""91, pp. 96-103, 1991 and J. Lai and F. Peng, xe2x80x9cMultilevel Convertersxe2x80x94A New Breed of Power Convertersxe2x80x9d, IEEE Transactions on Industry Applications, vol. IA-32, No. 3, pp. 509-517, 1996]. This is probably the best characteristic of the multilevel converters because the actual tendency is to improve the waveforms of the power electronic circuits.
The electromagnetic interference is smaller than that of conventional converters because the voltage variation (dv/dt) at the commutation instant is divided by the number of levels [T. A. Meynard and H. Foch, xe2x80x9cMulti-Level Conversion: High Voltage Choppers and Voltage-Source Invertersxe2x80x9d, Conference records of PESC""92, pp. 397-407, 1992]. In the European countries there is already a strict norm to limit the electromagnetic interference and other counties will follow their example.
An interesting configuration for a three-phase three-level rectifier has been considered lately by several researchers [See Ewaldo L. M. Mehl and Ivo Barbi, xe2x80x9cAn Improved High Power Factor and Low Cost Three-Phase Rectifierxe2x80x9d, Conference records of APEC""95, pp. 835-841, 1995; and J. W. Kolar, H. Ertl and F. C. Zach, xe2x80x9cDesign and Experimental Investigation of a Three-Phase High Power Density High Efficiency Unity Power Factor PWM (VIENNA) Rectifier Employing a Novel Integrated Power Semiconductor Modulexe2x80x9d, Conference records of APEC""96, pp. 514-523, 1996]. The converter is composed by a combination of diodes and switches adjusted to the requirements of generating an input current nearly sinusoidal with high power factor and low total harmonic distortion while achieving the requirements of high efficiency, high reliability and controllable output voltage.
So far several control schemes for the three-phase three-level boost type rectifier have been proposed. In the control method proposed in [Ewaldo L. M. Mehl and Ivo Barbi, et al., op. cit.], the active switches are gated at the line frequency. The bi-directional switches are gated on at zero crossing of the corresponding phase-voltage. The open loop control is simple and total harmonic distortion may reach acceptable levels at certain point of operation. However, does not allow output voltage control and the harmonic distortion may increase if the conduction angle of the switches is chosen to be different than 30 degrees. Therefore, the applications for this type of control are reduced.
Authors of [F. Daniel, R. Chaffai and K. Al Haddad, xe2x80x9cThree-Phase Diode Rectifier with Low Harmonic Distortion to Feed Capacitive Loadsxe2x80x9d, Conference records of APEC""96, pp. 932-938, 1996] made some improvements in that control, but the controllability of the output voltage is still a drawback.
The methods introduced in [Yifan Zhao, Yue Li, and Thomas A. Lipo, xe2x80x9cForce Commutated Three Level Boost Type Rectifierxe2x80x9d, IEEE Transactions on Industry Applications, vol. IA-31, No. 1, pp. 155-161, 1995] and [J. W. Kolar and F. C. Zach, xe2x80x9cA Novel Three-Phase Three-Switch Three-Level Unity Power Factor PWM Rectifierxe2x80x9d, Conference records of PCIM""94, pp. 125-138, 1994] are based in advanced space vector control and both make use of complex digital logic, implemented with digital signal processors.
Another similitude of both techniques is the use of hysteresis controllers. Those control methods feature low input current harmonics, balance of the center point of the output voltage and high controllability of the output voltage. The disadvantages of the mentioned methods are: complex and expensive DSP-based control, complicated design of the input EMC filter due to the varying switching frequency (inherent problem of hysteresis controllers) and the current control error may be twice the hysteresis width as stated in [J. W. Kolar and F. C. Zach, et al., op. cit.].
The technique proposed in [P. Prestifilippo, R. Scibilia, G. Baggione, G. Caramazza, xe2x80x9cA Switched-Mode Three-Phase 200A/48V Rectifier with Input Unity Power Factorxe2x80x9d, Conference records of INTELEC""96, pp. 543-547, 1996] consider the three-phase rectifier as three single-phase units and the control is implemented using commercial single-phase modulators with three independent current loops. The control is simple, but the input current ripple is much higher than that of the vector controls discussed above. Moreover, since three independent current loops are used it is not possible to synchronize the command signals of the switching devices and this compromise the control performance. Similar technique was used in [R. Gules, A. S. Martins and I. Barbi, xe2x80x9cA Switched-Mode Three-Phase Three-Level Telecommunications Rectifierxe2x80x9d, Conference records of INTELEC""99, paper 29-3, 1999] but no further improvements were presented.
Finally, an interesting control method was presented in [P. Ide, N. Froehleke, H. Grotstollen, xe2x80x9cInvestigation of low cost control schemes for a selected 3-level switched mode rectifierxe2x80x9d, Proceedings of INTELEC""97, pp. 413-418, 1990], the double ramp comparison control concept was used, synchronizing the main devices command signals and therefore simplifying the EMC filter, reducing also the input current ripple. However, the control system needs to generate a sinusoidal function in order to balance the output voltages. The generation of this function may complicate the control because its phase and frequency must be synchronized with the mains.
In this work a new control method for the three-phase three-level boost-type rectifier will be introduced with the objective of solving the drawbacks presented by the above mentioned techniques.
3xe2x80x94Objectives of the Invention
The present invention introduces a new control scheme for a three-phase three-level boost-type rectifier with reduced input current ripple and balanced output voltages. The principal objective of the proposed technique is to simplify the control circuit as much as possible without compromising the rectifier performance. In fact, besides simplicity, the control method features synchronized command signals to de switching devices, minimized input current ripple, full controllability of the output voltage, dynamic balance of the output center point, constant switching frequency, simplified design of EMC filters, good transient and steady state performance, and low cost.
The control system uses two triangular carriers namely Trg1 and Trg2. The carriers have the same amplitude but are 180 degrees phase-shifted; Trg1 is used during the positive halve cycle of the respective phase voltage and Trg2 for the negative one. An analog switch in each phase permits the interchange among the triangular carriers. The switching devices command signal is obtained comparing the respective reference with the carriers. Thus the switching frequency is constant. The output center point balance is achieved by adding the positive and negative output voltages and using the sum as an error signal to modify the current waveform reference. This simplifies the control circuit and allows an accurate regulation of the center point potential.
The control system retains all the advances of multilevel converters. When compared with conventional two level systems, the proposed converter is characterized by a lower blocking voltage of the switching devices, lower harmonic distortion on the line currents, lower EMI rejected noise, absence of shoot-through current and offer positive and negative output voltages.
Compared with the techniques developed in [Ewaldo L. M. Mehl and Ivo Barbi, at al., op. cit.], and [F. Daniel, et al., op. cit.], the proposed method increases greatly the controllability of the output voltages and reduces the low frequency distortion. Advantages with respect to vector-control schemes of [Yifan Zhao, et al., op. cit.], and [J. W. Kolar et al., op. cit.], are simplified and cheaper control, and constant switching frequency, which facilitate the EMC filter design. The new technique offer lower input current ripple than methods based in three independent controllers such as those of [P. Prestifilippo, et al., op. cit.], and [R. Gules, et al., op. cit.]. The simplicity of the control of neutral potential can be considered as improvement with respect to the method presented in [P. Ide, et al., op. cit.].
II. 1. Three-Phase Three-Level Boost-Type Rectifier Circuit Description and Operation.
The three-phase three-level boost-type rectifier may have different configurations, FIG. 1 shows four of the most interesting ones, but the principle of operation is basically the same for all of them. Although the circuits of FIGS. 1(a) and (c) have three more switches (S4, S5, and S6), they are activated with the same command of S1, S2 and S3 respectively. Therefore, when S1 is activated, the input terminal xe2x80x9cuxe2x80x9d is clamped with the DC-link neutral point xe2x80x9cOxe2x80x9d and euO=0. When the switch is open, the direction of the input current determines the euO potential difference. The terminal xe2x80x9cuxe2x80x9d will be clamped with xe2x80x9cPxe2x80x9d if iu is positive (euO=Ed); and with xe2x80x9cNxe2x80x9d if iu is negative (euO=xe2x88x92Ed). The analysis is also valid for the other switching arms and applies to all four topologies. A common equivalent circuit can be drawn as shown in FIG. 2. According with the switching state of the power semiconductors, each input terminal has three possible states; therefore, the three-phase system has 3xc3x973xc3x973=27 possible states. The states are listed in Table 1 below, which also gives the respective voltages referred to the neutral point.
It can be noted that the maximum voltage stress in the power switches is only half of the DC-link voltage (Ed); this allows the use of faster and cheaper devices. Another significant advance is that there is no possibility of shot-though current on the rectifier arms, which simplifies the gating of the switches.
The switching states can be considered as space vectors, which components are placed in three axes, namely euO, evO and ewO, separated 120 degrees from each other. The space vector representation is a useful tool to generate advanced PWM (Phase Width Modulation). It helps to visualize the amplitude and phase of the voltage vectors. The space vector representation of the switching states of the three-phase three-level boost-type rectifier is shown in FIG. 3.
The voltage vectors have been classified in five groups. The big size vectors are associated in group xe2x80x9caxe2x80x9d they are characterized because the input terminals are clamped to the positive terminal xe2x80x9cPxe2x80x9d or the negative terminal xe2x80x9cNxe2x80x9d, with no connection to the neutral point. The group xe2x80x9cbxe2x80x9d corresponds to the medium size vectors; their amplitude is reduced because one of the input terminals is clamped to the neutral point.
Groups xe2x80x9ccxe2x80x9d and xe2x80x9cdxe2x80x9d refer to the small vectors. The input terminals are clamped to xe2x80x9cPxe2x80x9d and xe2x80x9cOxe2x80x9d in the case of group xe2x80x9ccxe2x80x9d and therefore are called small positive group. In the small negative group (xe2x80x9cdxe2x80x9d) the input terminals are clamped to xe2x80x9cNxe2x80x9d and xe2x80x9cOxe2x80x9d. The last set corresponds to the zero vectors, group xe2x80x9czxe2x80x9d; the three input terminals are clamped to the same output point xe2x80x9cOxe2x80x9d, xe2x80x9cNxe2x80x9d or xe2x80x9cPxe2x80x9d.
II. 2. Control Methods.
If the converter output voltage is considered constant, the rectifier can be treated as voltage source connected to the utility through the input inductors as shown in the equivalent circuit of FIG. 4. The following relations can be writing by inspection of FIG. 4:                               e          an                =                                            L              u                        ·                                          di                u                            dt                                +                      e            un                                              (        1        )                                          e          bn                =                                            L              v                        ·                                          di                v                            dt                                +                      e            vn                                              (        2        )                                          e          cn                =                                            L              w                        ·                                          di                w                            dt                                +                      e            wn                                              (        3        )            
Form (1)xcx9c(4) it is clear that it is possible to control the input current by taking action on the rectifier input terminal voltage. From fundamental circuit theory it can be determined that for the input current to be sinusoidal, the input terminal voltages eun, evn and ewn must be sinusoidal as well. Using the concept of instantaneous mean value, it is necessary to generate sinusoidal PWM waveforms at the rectifier input-terminals, in other words, those voltages should be controllable in order to control the amplitude and phase angle of the input current.
It is well known that vector control schemes allow the generation of high quality waveforms, then it is possible to use the vector analysis as a useful tool to find an improved waveform generation. Let us review more deeply the space vector plane of FIG. 3. For symmetry it is enough to consider only one 60 degrees interval. There is a restriction that limits the number of possible vectors at any instant. Consider for example that the instantaneous current in one leg is positive, then the related input terminal can be clamped to the positive terminal if the switch is off and to the neutral terminal if the switch is on, but can no be clamped to the negative terminal.
Table 2 below lists the available vectors in the first 60 degrees interval and the respective switching state. It has been considered that the input current is in phase with the respective source voltage.
FIG. 5 shows the space vector representation for the first 60 degrees interval. A sinusoidal three-phase voltage waveform is represented in the space plane as a circle; the radius of the circle is related to the voltage amplitude.
At any instant, the points of the circle should de generated by a combination of the available vectors. For a switching frequency high enough, the medium value in a period can be considered as a point in the space plane A single vector can only generate one point; combining two vectors and changing their dwell time, the straight line that link tem can be generated. Then, to generate any point inside a sector, at least three vectors are needed.
Advanced vector control schemes divides the space plane in triangular sectors and the sinusoidal PWM waveform is generated by switching among the three vectors that correspond to the apices of the triangle that contains the respective point of the circle at that instant. [R. Rojas, T. Ohnishi, T. Suzuki, xe2x80x9cAn Improved Voltage Vector Control Method for Neutral-Point-Clamped Invertersxe2x80x9d, IEEE Transactions on Power Electronics, vol. 10, No 6, pp. 666-672, 1995].
For area 1 in FIG. 5, the vectors used are {right arrow over (c)}5 (OOP), {right arrow over (b)}6 (ONP), {right arrow over (c)}6 (POP) and {right arrow over (d)}6(ONO). Generally this is executed by using hysteresis controllers and complicated look-up tables. The major problem associated with hysteresis control is that the switching frequency varies throughout the AC supply cycle.
In order to fix the switching frequency, carriers should be used to modulate the pulse width. A method that uses saw-tooth carriers to obtaining the command signals is illustrated in FIG. 5. The current reference is compared with the respective high-frequency saw-tooth carrier. To simplify the analysis the three carriers are supposed to be synchronized. The iu*, iv* and iw* signals represent the output of the respective current controller (modulating signal); they are supposed to be constant during the switching period. As can be seen from the figure there are 4 switching states per period, corresponding to the vectors {right arrow over (z)} (OOO), (ONO), (ONP) and (PNP). Certainly those vectors give a picture of a bigger triangle in the space vector representation plane which results in lower quality of the waveform generation.
To overcome the drawbacks of the former mentioned techniques a different approach is considered in this work. The modulating signals are fed together with two high-frequency triangular carriers to the pulse-with modulator. The two carriers are of the same amplitude but 180 degrees phase-shifted; the first is used during the positive half cycle of the utility sinusoidal voltage and the other during the negative one. The principle of this technique is illustrated in FIG. 7. The modulating signals iu* and iw* are compared with Trg1 because the corresponding source voltages are positive during this interval (0xcx9c60 degrees) and iv* is compared with Trg2 because it is negative. It is clear from FIG. 3 that with the same switching frequency the new control method generates eight states per period due to an appropriate distribution of the command pulses. The vectors used are (PNP), (ONP), (POP) and (ONO) which match up with the vectors selected by advanced vector control methods. Consequently, the input current ripple will be smaller with the new proposed control and having the advantage of constant switching frequency. Moreover, the xe2x80x9capparent switching frequencyxe2x80x9d is twice as that of the former control method because there are eight states per period instead of four.
II. 3. Output Voltages"" Balance.
The neutral point potential is not a rigid voltage source; it is generated by the series connection of the DC-link capacitors. Thus, it is not certain that the two output voltages will remain equal. On the contrary, the neutral point potential will increase or decrease according to the charging-discharging action of the capacitors.
However, the capacitor voltages should be maintained in balanced condition to guarantee the true three-level operation throughout the whole range of voltage control. If it is violated the output may contain undesirable harmonic; moreover, if the neutral point potential deviates of its balanced condition the voltage over the switching devices or the capacitors may increase over their ratings and it makes impossible to operate the converter any longer; irreparable damages may occur.
Different from hysteresis based control methods, the proposed modulation technique is well symmetrical; therefore, symmetrical charge of the capacitors can be expected. Load is usually symmetrical as well, but slight imperfections in the circuit may promote neutral point voltage drift. Therefore, explicit control over the neutral point voltage must be implemented together with input current control.
Neutral point potential deviations are related with the process of charge and discharge of the DC-link capacitors. The input current gives the capacitor charge through the power semiconductor devices. The five groups of vectors produce different charge currents in the capacitors.
The connection between utility and DC-link capacitors for the five groups of vectors is illustrated in FIG. 8. The vectors of group xe2x80x9caxe2x80x9d does not present any connection with the neutral point (xe2x80x9cOxe2x80x9d), therefore, the charge current is the same for both capacitors. On the other hand, no charge current is given to the capacitors when using vectors of group xe2x80x9czxe2x80x9d.
Different capacitor charge takes place only for vectors of groups xe2x80x9cbxe2x80x9d, xe2x80x9ccxe2x80x9d, and xe2x80x9cdxe2x80x9d; this fact can be exploited to control the neutral point potential. From FIG. 8 it is clear that a vector of group xe2x80x9ccxe2x80x9d charges capacitor C1 and a vector of group xe2x80x9cdxe2x80x9d charges capacitor C2.
Since vectors of groups xe2x80x9ccxe2x80x9d and xe2x80x9cdxe2x80x9d generate the same rectifier input terminal voltage, interchanging between them do not alter the input current control. Therefore, the neutral point potential can be controlled by acting on the dwell time of vectors of groups xe2x80x9ccxe2x80x9d and xe2x80x9cdxe2x80x9d.
The same principle may be used for other advanced modulation techniques; however they differ in the way of controlling the dwell times. A number of methods to carry out the control has been considered, one of them using an additional hysteresis controller together with look-up tables, another method uses a cosine curve with a frequency three times the main frequency (utility).
The invention described here proposes to add a quantity proportional to the deviation to the input current reference waveform. In such a way a DC value will be added or subtracted to the modulating signal for the positive or negative halve cycle of mains voltage respectively.
After comparison with the triangular carrier, this will reflect in an increase of the xe2x80x9ccxe2x80x9d group vector dwell time and a decrease of the xe2x80x9cdxe2x80x9d group vector dwell time without altering the dwell time of other vectors. This fact is illustrated in FIG. 9; in FIG. 9(a) a small DC quantity was added to the reference signals and in FIG. 9(b) the same value was subtracted. Notice that the dwell time of vectors {right arrow over (c)}5 (OOP) and {right arrow over (b)}5 (ONP) remain inalterable whereas the dwell time of (POP) reduces in FIG. 9(a) and increases in FIG. 9(b). The opposite situation occurs with (ONO), which increases in FIG. 9(a) and reduces in FIG. 9(b).
II. 4. Control System.
The block diagram of the control system is given in FIG. 10. Analogue control signals are derived from the utility voltage, input current and from the output voltages. These signals are conditioned and combined to form the modulating signals that are fed, together with two high-frequency triangular carriers, to the pulse-width modulators. The digital outputs of the modulators provide the drive signals for the converter power switches. More details of the control blocks will now be described.
Referring to FIG. 10, a signal representing the output capacitor voltages is derived from a potential divider (1) and subtracted in (2) to obtain the total output voltage. This signal is compared with a DC reference voltage and regulated with a compensator (3), which generate the amplitude of the current reference.
The waveform of the current reference is derived from the utility voltage, which is sensed from potential dividers (4). Since the mains neutral is not available, an analog circuitry (5) is used to obtain the phase-voltage waveforms. This circuitry also gives the logic signals to discriminate the positive half cycle from the negative one. The sum of the positive and negative output voltages given by (6) represents the deviation of the neutral potential form its balanced condition. This signal is added to the phase voltages to obtain the balance control as explained above.
After the summing block (7) the signals are rectified in (8) to generate the current waveform reference. The current references are obtained by multiplying in (9) their common amplitude by the respective waveform; this signal represents a sinusoidal current proportional to the voltage error.
The actual currents are derived using current transformers with Hall-effect sensor (10) and then rectified in (11). The modulating signals are derived from analog controllers (12) that compare the respective actual and reference current to generate a compensation signal. Analog signal-switches (13) are used to exchange the two triangular carriers; the analog switch commands are given by (5).
The modulating and carrier signals are fed to a pulse-width modulator (14), which generates the drive signal for the respective converter power switch.